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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 181515, 16124]*) (*NotebookOutlinePosition[ 182417, 16155]*) (* CellTagsIndexPosition[ 182373, 16151]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " code and figures created for the paper \"Understanding the Back \ Propagated Neural Network Using ", StyleBox["Mathematica", FontSlant->"Italic"], " Graphics\"\nSteve Hunka, University of Alberta; steve.hunka@ualberta.ca\n\ Mike Carbonaro" }], "Section", Evaluatable->False, AspectRatioFixed->True, FontSize->14], Cell[TextData["Date Last Modified: Apr 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If p is any integer then an integer is to be input; if p is any real \ value then a real value is to be input; if p={n} then a n element vector is \ expected; if p={r,c} then a matrix with r rows and c columns is expected. If \ the input is inappropriate the question is posed again. If the input is \ appropriate it is returned."], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "kbin3[q_,p_]:=\n Module[{c,ans,vrp,vrp2},\n c=0;\n vrp=\" Input Error. \ Type a vector with # elements=\";\n vrp2=\" Input Error. 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Date: March 24/97"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "inpvec[r_,n_,ty_]:=Module[{q,selv,rng},\nq=\"Type element vector of .\";\n\ q=StringInsert[StringInsert[q,ToString[n],6],ty,-2];\nrng=False;\n\ While[rng==False,\n selv=kbin3[q,{n}];\n If[Max[selv]>Max[r] || \ Min[selv]True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "kbinstrg[q,p] used to input a string in response to question in q. p \ contains acceptable answers in the form of a list,eg., \ p={{ans1},{ans2},....}. If the input is appropriate it is returned. If the \ input is inappropriate the question is posed again."], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "kbinstrg[q_,p_]:=\n Module[{c,ans},\n c=0;\n While[c==0,\n \ ans=InputString[q];\n Do[If[{ans}==p[[j]],\n c=1; Break[]];\n \ ,{j,1,Length[p]}]; (* end Do *) \n If[c!=1,Print[ans,\" Input Error. Type \ Again\"]]; \n ]; (*end While*)\n Return[ans];\n ]; (* end Module*)"], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "getFdata:The user is asked to input the name of the file holding the file \ data; if the file is found a message is given; if the file is not found a \ message is given and the user is asked to give another name. If the user \ enters quit at the point of entering a file name, the function stops. If the \ file is available the user is asked whether \"all\" or only \"part\" of the \ data is to read. If the user enters all, all data is used; if part is \ entered, the user is asked to give the starting point in the file and the \ ending point for which the data is wanted.\nCalls: kbin3, kbinstrg,timeDate\n\ Returns: data from the file read, and extnt a 2 element vector of starting \ and\n ending position for the data read. "], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "getFdata:=\n Module[{fname,ok,data,extnt,strt,end},\nok=0;\n While[ok==0,\n \ fname=InputString[\"Type name of file\"];\n If[fname==\"quit\",Return[]];\n \ If[{fname}===FileNames[fname],\n Print[fname,\" was found\"];ok=1;\n \ ,Print[fname,\" was not found\"]];\n ]; (*end While *)\n Print[\"File \ created:\"];\n timeDate[FileDate[fname]];\n extnt=kbinstrg[\"Use all or part \ of data file?\",\n {{\"all\"},{\"part\"}}];\n Print[\"Data read from \ file=\",extnt];\n If[extnt==\"all\",data=ReadList[fname];\n \ extnt={1,Part[Dimensions[data],1]}; (*else*)\n ,strt=kbin3[\"Type starting \ position\",0];\n end=kbin3[\"Type ending position\",0];\n OpenRead[fname];\n\ Skip[fname,Expression,strt];\n data=ReadList[fname,Expression,1+end-strt];\ \n Close[fname];\n Print[\"Data returned from file=\",strt,\" to \",end];\n \ extnt=ToString[Join[{strt},{end}]];\n ]; (*end if extnt*)\n Print[\"Returned \ data dimension=\",Dimensions[data]];\n Return[{data,extnt}];\n ]; (*end \ Module*)"], "Input", AspectRatioFixed->True], Cell[TextData[ "General::spell1: \n Possible spelling error: new symbol name \"end\"\n \ is similar to existing symbol \"End\"."], "Message", Evaluatable->False, AspectRatioFixed->True] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "timeDate[ts] prints month day,year at hour:minutes. ts is vector returned by \ Date or FileDate."], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "timeDate[ts_]:=\n Module[{month},\n month={{\"Jan \"},{\"Feb \"},{\"Mar \ \"},{\"Apr \"},\n {\"May \"},{\"Jun \"},{\"Jul \"},{\"Aug \"},\n \ {\"Sep \"},{\"Oct \"},{\"Nov \"},{\"Dec \"}};\n \ Print[Part[month,ts[[2]]][[1]],ts[[3]],\",\",ts[[1]],\n \" at \ \",ts[[4]],\":\",ts[[5]]];\n ];\n "], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "splt3d[d_,ttl_] 3D plot for weights or output of 3 cells defined by user. \n\ d is the cell output or weights from the neural network usually stored in a \ file;\nttl is a title for the plot.\nThe user input options are:\na) whether \ each plot should be marked with an id number at the start or end of\n the \ line or dots plotted.\nb) whether lines or points are to be plotted; if \ points, the point size is\n requested.\nc) whether single 3d plots should \ be made in addition to the combined plot\n ScatterPlot3D produces \ Graphics3D[{Point[{x,y,z}],.....},options]; it is\n changed to give \ Graphics3D[{PointSize[ps],Point[{x,y,z}],.....},options\n in each \ pobj[[j]]. Also the first or last point is changed to Text[j,{x,y,z}]\n \ depending upon option (a) above.\nd) the cell data to use, e.g., {1,2,5} \ plots point as defined by cells 1, 2 and 5. \ne) whether more plots are \ wanted after the first, to allow user to select other\n cells.\n Note: \n \ 1)PlotRange->All has been set. If PlotRange->Automatic, then if in (a) \ \"end\" is selected an id number may not appear for a specific plot because \ the plot was truncated.\n 2) d is of order (#epochs, #z,#hidden cells) where \ #z may be number of output cells, number of exemplars, or number of input \ cells depending on the calling function. \nCalls: kbinstrg, kbin3,inpvec\n\ Rqrs: <False, AspectRatioFixed->True], Cell[TextData[ "splt3d[d_,ttl_]:=\n Module[{p,ans,ln,pobj,temp,ps,ept,ipt,hcv,dt,qplt},\n \ ept=Part[Dimensions[d],1];(*default mark end point*)\n \ p=Part[Dimensions[d],2];\n (*dt=Transpose[d,{3,1,2}];*)\n qplt=\"y\";\n \ While[\"y\"==qplt, \n ans=kbinstrg[\"Mark start or end?\",\n \ {{\"start\"},{\"end\"}}];\nPrint[\"Line id=\",ans];\n\ If[ans==\"start\",ept=1];\n ans=kbinstrg[\"Join plotted points? \ y/n\",{{\"y\"},{\"n\"}}];\nIf[ans==\"n\",ln=False;\n ps=kbin3[\"Type point \ size\",0.01];\n Print[\"Point size=\",ps];\n ,ln=True;];\n\ ipt=kbinstrg[\"Single plots? y/n\",{{\"y\"},{\"n\"}}];\n\ If[ipt==\"y\",ipt=$DisplayFunction,ipt=Identity];\n\ hcv=inpvec[{1,Part[Dimensions[d],3]},3,\"hidden cells\"];\nPrint[\"Selected \ Cells=\",hcv];\n pobj=List[]; \ndt=Transpose[d,{2,3,1}][[hcv]];\n\ dt=Transpose[dt,{3,2,1}];\n pobj=MapThread[\n ScatterPlot3D[#,\n \ PlotJoined->ln,Axes->True,\n AxesLabel->Map[ToString,hcv],\n \ PlotRange->All,\n DisplayFunction->ipt]&,\n {dt}]; \n If[ans==\ \"n\",\n Do[ (*incl ps in each graphic object*)\n \ temp=Append[{PointSize[ps]},pobj[[j]][[1]]];\n \ pobj=ReplacePart[pobj,temp,{j,1}];\n pobj=pobj /.\n pobj[[j,1,2,ept]]->\ \n Text[ToString[j],pobj[[j,1,2,ept,1]]];\n ,{j,1,p}];,\n (* do below \ if ans==y, ie lines *)\n Do[\n temp=Append[{Text[ToString[j],\n \ pobj[[j,1,1,ept]]]},pobj[[j,1]]];\n \ pobj[[j]]=ReplacePart[pobj[[j]],temp,1];\n ,{j,1,p}];\n ];\n Show[pobj,\n\ PlotLabel->ttl, \n DisplayFunction->$DisplayFunction];\n \ qplt=kbinstrg[\"More plots? y/n\",{{\"y\"},{\"n\"}}];\n ]; (*end While *)\n \ ]; (* end Module *)\n \n "], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "hdwAray[d___]: used for making an array plot of the hidden cell weights by \ epoch for each input cell (attribute).\nd is optional; if d is present it \ contains the hidden weights of order (#epochs,#hidden cells,#input cells). d \ may be obtained from the appropriate file created by the neural network \ program bpnn by using ReadList[\"filename\"]. If d is absent, the user is \ requested to give the name of the file holding the hidden weights. \n\nEach \ plot contains one colored line for each hidden cell, and each plot represents \ a different attribute of the exemplars input. The plots are brought together \ in an array of plots for which the user may specify a common y-axis scaling \ (or default the scaling) and the plot arrangement. If the number of plots in \ each row exceeds the number of plots available an error message is given.\n\ User Input: \n1) See getFdata if hdwmulist[] is used.\n2) plot range (y/n); \ if y, {min,max} required; if no PlotRange->All\n3) a vector specifying the \ number of plots in each row of the array plot. The sum of the elements in \ this vector should equal the number of input cells.\nCalls: mplotLists, \ araydis, kbinstrg, kbin3,getFdata, timeDate\n\ Required:<False, AspectRatioFixed->True], Cell[TextData[ "hdwAray[d___]:=\n Module[{data,extnt,nhc,nic,p,prng,ans,lim,apat,ok},\n \ Print[\"Hidden Weights,Plots=inc[j]\"];\n Print[\"Yaxis=wt; Xaxis=epoch; \ Line=hc[j]\"];\n Print[\"Point=wt at each epoch\"];\n If[Length[{d}]==0,\n \ {data,extnt}=getFdata;,data=d];\n nhc=Part[Dimensions[data],2];\n \ nic=Part[Dimensions[data],3];\n Print[\"Number Hidden cells=\",nhc];\n Print[\ \"Number of input cells=\",nic];\n Print[\"Minimum weight=\",Min[data]];\n \ Print[\"Maximim weight=\",Max[data]];\n p=List[];\n ans=kbinstrg[\"Set plot \ range? y/n\",{{\"y\"},{\"n\"}}];\n If[ans==\"y\",\n prng=kbin3[\"Type \ {min,max} plot range\",{2}];,\n prng=All];\n Do[ (* over number of input \ cells *)\n AppendTo[p,mplotLists[Transpose[\n \ Transpose[data,{3,2,1}][[i]]],prng]]; \n ,{i,1,nic}]; (*end Do *)\n \ \n ok=0;\n While[ok==0,\n apat=Input[\"Type vector of # plots in each row \ of array\"];\n If[Apply[Plus,apat]>Length[p],\n Print[\"Error: too many \ plots in vector\"];,\n ok=1]; (*end if *)\n ]; (*end while *)\n (*now \ display plots according to pattern in apat*)\n Show[GraphicsArray[\n \ araydis[Flatten[p],apat]],\n DisplayFunction->$DisplayFunction]; \ \n ]; (*end Module *)"], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "mplotLists[m]; plots the values in the columns of a 2 dimensional matrix m \ using MultipleListPlot, but the plotting symbols are removed; up to 12 \ different colors are used to plot the lines after which the color cycle \ repeats.\n$LineStyles is changed. The colors are rotated through the \ following color sequence:(1) black, (2) blue (3) green, (4) cyan, (5) red, \ (6) magenta,\n(7) yellow, (8) dark blue, (9) dark green (10) turquoise, \ (11)brown, and (12)\npurple. (Colors numbered 8 to 12 may vary with different \ monitors.) lim is a 2 element vector of min and max plot range or All to \ default the plot range of y. \nRequires: <False, AspectRatioFixed->True], Cell[TextData[ "mplotLists[m_,lim_]:=\nModule[{pobj,mtr,indx,nr,lstyl,colr},\n pobj=List[]; \ \n mtr=Transpose[m];\n nr=Part[Dimensions[mtr],1];\n \ lstyl=Table[{Thickness[0.005],RGBColor[0,1,0]},{nr}];\n \ colr={0.,0.,0.,0.,0.,1.,0.,1.,0.,0.,1.,1.,\n \ 1.,0.,0.,1.,0.,1.,1.,1.,0.,\n \ .0,.0,.5,.0,.5,.0,.0,.5,.5,.5,.0,.0,.5,.0,.5};\n Do[ (*replace RGB color \ parameters *)\nlstyl[[j]]=ReplacePart[lstyl[[j]],RGBColor[\n \ colr[[1]],colr[[2]],colr[[3]]],{2}];\ncolr=RotateLeft[colr,3];\n,{j,1,nr}];\n\ $LineStyles=lstyl; (*Now set line styles*)\n\n(*Now get multiplelistplot \ graphics object*)\npobj=Apply[MultipleListPlot[##,\n \ AxesLabel->{\"x\",\"y\"},\n PlotJoined->True,\n PlotRange->lim,\n \ DisplayFunction->Identity]&,mtr];\n(*delete plot symbols for each plot \ according to indx*) \n\ indx=Transpose[{Table[1,{nr}],Range[nr],Table[1,{nr}]}];\n\ pobj=Map[Delete[#,indx]&,{pobj}]; \n\ (*Show[pobj,DisplayFunction->$DisplayFunction];*)\nReturn[pobj];\n]; (*end \ module*)\n \n"], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "plotnLists[m,tl,xu,ps,pm,pn] plots a colored line for each column of m. The \ values in the column are y coordinates and the x coordinates are taken to be \ from 1 to the number of rows of the matrix.\ntl is a title for the plot, \nxu \ is the label for the x-axis\nps set to 1 for individual plots for each col; \ 0 for no individual plots\npm set to 1 for one plot holding multiple lines; 0 \ for no plot\npn (Optional) set to 1 for line numbers at end of lines when \ pm=1; else 0 \nFor single plots (ps=1), the title is appended to a plot \ sequence number.\n The colors are rotated through the following color \ sequence:(1) black, (2) blue (3) green, (4) cyan, (5) red, (6) magenta, (7) \ yellow, (8) dark blue, (9) dark green (10) turquoise, (11)brown, and (12) \ purple. (Colors numbered 8 to 12 may vary with different monitors.) To get a \ simple example of the colors used, do \ plotnLists[Table[Range[0,11],{2}],\"Legend\",\"units\",0,1,1].\nMod. Date: \ Mar 20/97"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "plotnLists[m_,tl_,xu_,ps_,pm_,pn_:0]:=\nModule[{pobj,colr,ipt,cntr=0},\n\ If[ps==0 && pm==0,\n Print[\"Parameter error;no plot\"];Return[]];\n \ pobj=List[]; \n colr={.5,.0,.5,0.,0.,0.,0.,0.,1.,0.,1.,0.,0.,1.,1.,\n \ 1.,0.,0.,1.,0.,1.,1.,1.,0.,.0,.0,.5,.0,.5,.0,\n .0,.5,.5,.5,.0,.0};\n \ If[ps==1,ipt=$DisplayFunction,ipt=Identity]; \n \ pobj=MapThread[ListPlot[#,AxesLabel->{xu,\"y\"},\n \ PlotJoined->True,PlotRange->All,\n \ PlotLabel->StringInsert[tl,ToString[cntr=cntr+1],1],\n \ PlotStyle->{RGBColor[Part[colr=RotateLeft[colr,3],1],\n \ Part[colr,2],Part[colr,3]]},\n DisplayFunction->ipt]&,{Transpose[m]}]; \n \ If[pn==1, (*replace last point with number*)\n \ MapThread[AppendTo[pobj[[#,1]],\n Text[#,Last[pobj[[#,1,2,1]]]]]&,\n \ {Range[Length[Transpose[m]]]}];\n ]; (*end if*)\n \ If[pm==1,Show[pobj,PlotLabel->tl,\n DisplayFunction->$DisplayFunction]]; \ \n ]; (*end module*)\n \n"], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "araydis[m,in]; arranges the plots in m for GraphicsArray according to the \ arrangement specified by in. For example if m had 9 plots, and in={2,3,4} \ then the 1st row will contain 2 plots, the next 3 plots, and the last row 4 \ plots as displayed by Graphics Array."], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "araydis[m_,in_]:=\n Module[{pa,ma,nt},\n pa=List[];nt=Length[in];\n ma=m;\n\ Do[AppendTo[pa,Take[ma,in[[i]]]];\n ma=Drop[ma,in[[i]]];\n \ ,{i,1,nt}];\nReturn[pa];\n];"], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ "errAnlz: plots the error squared at each output cell as a single plot. The \ squared error data are read from a file written by the neural network \ simulation program bpnn, and is of order (#iterations,#outcells)\nUser Input: \ See function getFdata and plotnLists\nCalls: \ getFdata,timeDate,kbin3,kbinstrng,plotnLists\nNote: If there is wide \ variability in the values of error-squared for more than one output cell and \ a large number of iterations, a single plot of the error curves is likely to \ produce curves which appear to have solid colors throughout the range of the \ x-axis. In such cases, the RMS error output from the neural simulation \ function bpnn provides a better representation of the nature of the \ convergence towards minimum sqd error. \nMod. Date: Apr 17/97"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "errAnlz:= Module[{ttl,data,extnt,xunits},\nPrint[\"Plot of Sqd-error at \ Output Cells\"];\n{data,extnt}=getFdata;\nIf[0==extnt,Print[\"No data \ read\"];Return[]];\nttl=\" Sqd-error for Iterations=\";\n\ ttl=StringInsert[ttl,ToString[extnt],-1]; \n\ plotnLists[data,ttl,\"iterations\",1,0,0];\n]; (*end Module *) "], "Input", AspectRatioFixed->True] }, Open ]], Cell[TextData["Plot of squared error"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData["errAnlz"], "Input", AspectRatioFixed->True], Cell[TextData[ "Plot of Sqd-error at Output Cells\nerrfile was found\nFile created:\nOct \ 23,1995 at 10:5\nData read from file=all\nReturned data dimension={600, 1}"], "Print", Evaluatable->False, AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 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Plot is \ 3D of (hc1,hc2,hc3) at each epoch for each exemplar. Each dot is an epoch; \ each line is an exemplar; axes are hidden cell response values. 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.64392 Mdot P p .001 w .30997 .98373 Mdot P p .001 w .28398 .91585 Mdot P p .001 w .32353 .93271 Mdot P p .001 w .31043 .98214 Mdot P p .001 w .39723 .93124 Mdot P p .001 w .535 .63417 Mdot P p .001 w .49484 .63528 Mdot P p .001 w .31092 .98047 Mdot P p .001 w .57338 .36745 Mdot P p .001 w .5332 .46927 Mdot P p .001 w .28511 .91066 Mdot P p .001 w .52036 .66083 Mdot P p .001 w .32457 .92872 Mdot P p .001 w .5151 .45518 Mdot P p .001 w .31144 .97871 Mdot P p .001 w .36609 .64011 Mdot P p .001 w .4568 .57476 Mdot P p .001 w .54064 .65099 Mdot P p .001 w .39937 .92536 Mdot P p .001 w .28636 .90502 Mdot P p .001 w .31199 .97684 Mdot P p .001 w .3257 .92443 Mdot P p .001 w .56421 .31277 Mdot P p .001 w .41907 .61828 Mdot P p .001 w .31258 .97487 Mdot P p .001 w .28774 .89889 Mdot P p .001 w .32691 .91983 Mdot P p .001 w .53793 .44693 Mdot P p .001 w .3132 .97278 Mdot P p .001 w .40168 .91901 Mdot P p .001 w .28928 .89219 Mdot P p .001 w .5207 .43202 Mdot P p .001 w .31386 .97057 Mdot P p 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The data input is from the hidden weight file \ written by bpnn and is of order (#epochs, #hidden cells, #input cells).\nUser \ Input:\na) See getFile; splt3d user input is:\nb) whether lines to be \ identified at start or end\nc) whether plotted points are joined; if no, \ point size requested\nd) whether single plots for each line to be displayed\n\ e) indices of 3 hidden cells as a vector\nf) option to plot again with \ different hidden cells\nCalls: getFdata, kbin3, kbinstrng, splt3d\nRqd \ Packages: <False, AspectRatioFixed->True], Cell[TextData[ "hdwAnlz:=\n Module[{data,extnt,title},\n Print[\"Three Hidden Cell Weights \ for each Input cell\"];\n Print[\"Xaxis=hc[i] wt; Yaxis=hc[j] wt; Zaxis=hc[k] \ wt\"];\n Print[\"User specifies 3 hidden cells indices as vector\"];\n Print[\ \"Line[n]=inputcell[n]\"];\n {data,extnt}=getFdata;\n If[0==extnt,Print[\"No \ data read\"];Return[]];\n Print[\"Number of hidden \ cells=\",Part[Dimensions[data],2]];\n Print[\"Number of input \ 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